The work on \(\alpha \) -gapped palindromes was focused so far on combinatorial and algorithmic problems that extend the classical results obtained for squares and palindromes. Namely, problems like how many maximal \(\alpha \) -gapped repeats or palindromes does a word of length \(n\)  contain (here maximal means that the arms of the repeat cannot be both extended to the right or left with the same symbol), how efficiently can we compute the set of maximal \(\alpha \) -gapped repeats or palindromes of a word, how efficiently can we compute the longest \(\alpha \) -gapped repeat or palindrome, were investigated (see, for instance, [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, and the references therein). In this paper we obtain the following results:
